Question: Rewrite as a simplified fraction. ${0.\overline{63} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 63.6363...\\ 1x &= 0.6363...\end{align*}}$ Subtracting the two equations, we have: ${99x = 63}$ ${x = \dfrac{63}{99}} $ ${x = \dfrac{7}{11}} $